Latest compatible version of Classicube from the original GitHub repository (https://github.com/ClassiCube/ClassiCube) that can be compiled on Classicube for PowerMac PPC running Mac OS X 10.4.

third_party/fix16_sqrt.c

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+#include <stdint.h>
+/*-
+ * Copyright (c) 2019 Christophe Meessen
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE. */
+
+/*-
+ * Computing the square root of an integer or a fixed point integer into a fixed
+ * point integer. A fixed point is a 32 bit value with the comma between the
+ * bits 15 and 16, where bit 0 is the less significant bit of the value.
+ *
+ * The algorithm uses the property that computing x² is trivial compared to the
+ * sqrt. It will thus search the biggest x so that x² <= v, assuming we compute
+ * sqrt(v).
+ *
+ * The algorithm tests each bit of x starting with the most significant toward
+ * the less significant. It tests if the bit must be set or not.
+ *
+ * The algorithm uses the relation (x + a)² = x² + 2ax + a² to add the bit
+ * efficiently. Instead of computing x² it keeps track of (x + a)² - x².
+ *
+ * When computing sqrt(v), r = v - x², q = 2ax, b = a² and t = 2ax + a2.
+ *
+ * Note that the input integers are signed and that the sign bit is used in the
+ * computation. To accept unsigned integer as input, unfolding the initial loop
+ * is required to handle this particular case. See the usenet discussion for the
+ * proposed solution.
+ *
+ * Algorithm and code Author Christophe Meessen 1993. */
+
+static int32_t sqrt_fix16(int32_t value)
+{
+    uint32_t t;
+    uint32_t r = value;
+    uint32_t b = 0x40000000;
+    uint32_t q = 0;
+
+    while (b > 0x40) {
+        t = q + b;
+
+        if (r >= t) {
+            r -= t;
+            q = t + b; /* Equivalent to q += 2 * b */
+        }
+
+        r <<= 1;
+        b >>= 1;
+    }
+
+    q >>= 8;
+
+    return q;
+}
+